1. Field of the Invention
This invention is related in general to the field of scanning interferometry and, in particular, to an improved approach for signal acquisition by utilizing a pulsed light source.
2. Description of the Related Art
As well understood in the art of phase shifting and vertical scanning interferometry, the optical path difference (OPD) between a test beam and a reference beam is varied in order to make a measurement. This is typically accomplished by shifting either the test surface or the reference surface of the interferometer axially by a predetermined distance during or between times of acquisition of data frames. The shift is normally carried out in steps or by continuous motion at a known, ideally constant, speed.
In the stepping method, the sample surface (or, alternatively, the reference surface) is moved between data frames and held still during data acquisition; thus, the OPD is kept constant during acquisition of each data frame. In practice, the shift-and-hold motion of the stepping method is mechanically undesirable because a finite amount of time is required for the shifted portion of the apparatus to settle into a static condition, thereby slowing down the process of data acquisition. Therefore, this method is no longer generally preferred in the industry.
In the ramping method, the OPD is varied in a continuous, smooth fashion, typically by scanning either the sample surface or the reference surface at constant speed throughout the measurement sequence. This approach is more common for phase shifting and vertical scanning interferometry because it allows faster measurements than the stepping method. On the other hand, this approach has the disadvantage of continuously varying the OPD, which, in conjunction with the finite integration time required for the detector to acquire an adequate signal, necessarily results in a reduction of the detected fringe modulation signal with respect to the modulation of the light incident on the detector. This decreases the signal-to-noise ratio of the resulting data with a corresponding significant loss of measurement accuracy.
The reduction in the detected fringe modulation signal due to the detector""s integration time is well understood in the art and can be quantified analytically by the following equation:
xe2x80x83Idet(x,y)=Iinc(x,y){1+xcex3inc(x,y)sin c(xcex94/2xcfx80)cos[xcfx86(x,y)+xcex1i]}xe2x80x83xe2x80x83(1)
where Idet(x,y) is the intensity of the detected signal at the x,y pixel; Iinc(x,y) is the average intensity of the light signal incident on the detector over the detector""s integration time; xcex3inc(x,y) is the fringe modulation of the light incident on the detector; xcex94 is the phase shift, in radians, during the integration time; xcfx86(x,y) is the phase of the wavefront being measured; xcex1i is the average phase shift occurring during the frame time of data acquisition; and sin c(xcex94/2xcfx80)=sin(xcex94/2)/(xcex94/2).
Based on Equation 1, it is clear from the effect of the variable xcex94 that the ramping method of scanning produces a reduction in the detected fringe modulation of the light incident on the detector by the factor sin c(xcex94/2xcfx80). As illustrated in functional form in the plot shown in FIG. 1, longer integration times and correspondingly larger phase shifts produce greater reductions in the detected fringe modulation intensity. It is noted that Equation 1, which is written for a two-dimensional detector array (x,y), would apply in similar form to detectors of other dimensions, such as linear detector arrays.
The effect of the phase shift taking place when scanning is continued during the detector integration time is illustrated by the following table for phase shifts of xcfx80/4, xcfx80/2, 3xcfx80/4 and 3xcfx80/2, with a detector having an integration time of 33.3 milliseconds.
For simplicity of illustration, assuming xcex3inc(x,y) is equal to one (that is, the reference and test beams have exactly the same intensity), FIG. 2 shows the fringe modulation of the incident light and FIG. 3 the fringe modulation of the detected signal for the case where xcex94=3xcfx80/2 (Case 4), for example. In the case of white light, the fringe modulation shown in FIGS. 2 and 3 will also vary to some degree across the range of OPDs shown (i.e., it is maximum at zero OPD). The reduced modulation of the detected signal illustrates the loss of modulation resulting from the finite integration time of the detector. Thus, it is clear that this loss of signal is an undesirable consequence of the ramping method of scanning. This invention provides a procedure and apparatus for eliminating this inefficiency and improving the overall data gathering function of the instrument.
One primary objective of this invention is a method and apparatus for reducing the loss of signal produced by the finite integration time of detectors during phase-shifting and vertical-scanning interferometric measurements utilizing the ramping method of scanning.
Another important goal of the invention is a method and apparatus that improve data acquisition without reducing the scanning speed of the instrument.
Another objective of the invention is a procedure that can be implemented in conjunction with conventional feed-back loop control algorithms and/or hardware.
Still another objective is a method and apparatus that are suitable for incorporation within existing instruments.
A final objective is a procedure that can be implemented easily and economically according to the above stated criteria.
Therefore, according to these and other objectives, the preferred embodiment of the present invention consists of utilizing a pulsed light source in conjunction with a ramping scanning mechanism for phase-shift and vertical-scanning interferometry.
The pulse length and the scanning velocity are selected such that a minimal change in OPD occurs during the pulse. As long as the duration of the pulse is shorter than the detector""s integration time, the effective integration time and the corresponding phase shift are determined by the length of the pulse, rather than by the detector""s characteristics. The resulting minimal phase shift produces negligible loss of fringe modulation, thereby greatly improving signal utilization during phase-shifting and vertical-scanning interferometry.
Various other purposes and advantages of the invention will become clear from its description in the specification that follows and from the novel features particularly pointed out in the appended claims. Therefore, to the accomplishment of the objectives described above, this invention consists of the features hereinafter illustrated in the drawings, fully described in the detailed description of the preferred embodiment and particularly pointed out in the claims. However, such drawings and description disclose but one of the various ways in which the invention may be practiced.